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Renormalization of the QED of self-interacting second order spin 1/2 fermions
We study the one-loop level renormalization of the electrodynamics of spin
1/2 fermions in the Poincar\'e projector formalism, in arbitrary covariant
gauge and including fermion self-interactions, which are dimension four
operators in this framework. We show that the model is renormalizable for
arbitrary values of the tree level gyromagnetic factor g within the validity
region of the perturbative expansion, \alpha g^2 << 1. In the absence of tree
level fermion self-interactions, we recover the pure QED of second order
fermions, which is renormalizable only for |g|=2. Turning off the
electromagnetic interaction we obtain a renormalizable Nambu-Jona-Lasinio-like
model with second order fermions in four space-time dimensions.Comment: 32 pages, 9 figures. Published versio